Question: Find the greatest common factor of $21$ and $10$.
Explanation: The greatest common factor (GCF) is the largest number that is a factor of both $21$ and $10$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}21 &=3\cdot7\\\\\\\\ 10&=2\cdot5 \end{aligned}$ Since these numbers have no common prime factors, we say that the GCF is $1$. This is because all numbers share a factor of $1$ : $ \begin{aligned}21 &=3\cdot7\cdot1\\\\\\\\ 10&=2\cdot5\cdot1 \end{aligned}$ The greatest common factor of $21$ and $10$ is $1$.